Question 1186400: Two hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.
18 - 24 25 - 34 35 - 55 55 and over Total
Liked Crunchicles 1 6 5 6 18
Disliked Crunchicles 4 5 5 8 22
No Preference 38 5 9 108 160
Total 43 16 19 122 200
One consumer from the survey is selected at random. Use reduced fractions for your responses to each of the following questions.
What is the probability that the consumer is 18 - 24 years of age, given that they dislike Crunchicles?
What is the probability that the selected consumer dislikes Crunchicles?
What is the probability that the selected consumer is 35 - 55 years old or likes Crunchicles?
If the selected consumer is 70 years old, what is the probability that they like Crunchicles?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the probabilities based on the given table:
**1. Probability that the consumer is 18-24 years of age, given that they dislike Crunchicles:**
We are given that the consumer dislikes Crunchicles. So, we focus on the "Disliked Crunchicles" row. The probability that they are 18-24 years old is:
P(18-24 | Disliked Crunchicles) = (Number of 18-24 who disliked) / (Total who disliked)
P(18-24 | Disliked Crunchicles) = 4 / 22
P(18-24 | Disliked Crunchicles) = **2/11**
**2. Probability that the selected consumer dislikes Crunchicles:**
This is simply the number of people who disliked Crunchicles divided by the total number of people surveyed:
P(Disliked Crunchicles) = 22 / 200
P(Disliked Crunchicles) = **11/100**
**3. Probability that the selected consumer is 35-55 years old or likes Crunchicles:**
We need to consider the "35-55" column and the "Liked Crunchicles" row. However, we need to avoid double-counting the people who are both 35-55 years old and liked Crunchicles.
P(35-55 or Liked) = P(35-55) + P(Liked) - P(35-55 and Liked)
P(35-55 or Liked) = (19/200) + (18/200) - (5/200)
P(35-55 or Liked) = 32/200
P(35-55 or Liked) = **8/50 = 4/25**
**4. If the selected consumer is 70 years old, what is the probability that they like Crunchicles?**
Since the consumer is 70 years old, they fall in the "55 and over" category. We focus on that column.
P(Liked | 55 and over) = (Number of 55 and over who liked) / (Total 55 and over)
P(Liked | 55 and over) = 6 / 122
P(Liked | 55 and over) = **3/61**
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